Skip to Main Content

Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Generic extensions and multiplicative bases of quantum groups at ${{\mathbf q=0}}$
HTML articles powered by AMS MathViewer

by Markus Reineke PDF
Represent. Theory 5 (2001), 147-163 Request permission


We show that the operation of taking generic extensions provides the set of isomorphism classes of representations of a quiver of Dynkin type with a monoid structure. Its monoid ring is isomorphic to the specialization at $q=0$ of Ringel’s Hall algebra. This provides the latter algebra with a multiplicatively closed basis. Using a crystal-type basis for a two-parameter quantum group, this multiplicative basis is related to Lusztig’s canonical basis.
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 17B37, 16G30
  • Retrieve articles in all journals with MSC (2000): 17B37, 16G30
Additional Information
  • Markus Reineke
  • Affiliation: BUGH Wuppertal, Gaußstr. 20, D-42097 Wuppertal, Germany
  • MR Author ID: 622884
  • Email:
  • Received by editor(s): August 14, 2000
  • Received by editor(s) in revised form: April 10, 2001
  • Published electronically: June 12, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Represent. Theory 5 (2001), 147-163
  • MSC (2000): Primary 17B37; Secondary 16G30
  • DOI:
  • MathSciNet review: 1835003